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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

The velocity, v, in feet per second, t sec after a tennis ball is projected directly upward is given by the formula v = 84 - 32t. How many seconds after being projected upward will the velocity be
For a business to realize a profit, its revenue, R, must be greater than its costs, C; that is, a profit will result only if R > C (the company breaks even when R = C). A dry cleaning store has a
A parking garage in Richmond, Virginia, charges $1.75 for the first hour and $0.50 for each additional hour or part of an hour. What is the maximum length of time Tom can park in the garage if he
The Kubys are celebrating their 75th wedding anniversary by having a party at the Diplomat Party House. They have budgeted $4000 for the party. If the party house charges a flat rate of $100 for
To be eligible for financial assistance for college, Samantha can earn no more than $3200 during her summer employment. She will earn $662.50 cutting lawns. She is also earning $7.25 per hour at an
Bobby recently accepted a sales position in Portland, Oregon. He can select between the two salary plans shown in the table. Determine the dollar amount of weekly sales that would result in Bobby
FitForLife gym offers two member-ship options. Option A requires an initial membership fee along with a monthly payment. Option B requires only a monthly payment. The two membership options are shown
The following graph shows the unemployment rate in the United States for the years 2005€“2013.In which years, from 2005€“2013, was the unemployment rate in the United States.(a)
The following graph shows the total motor vehicle production, in millions, in the United States for the years 2006€“2013.In which years was the number of vehicles produced(a) > 8.5
Graph the solution set of the inequality, where x is an integer, on the number line.-1/3 < (x - 2)/12 ≤ 1/4
Graph the solution set of the inequality, where x is an integer, on the number line.0.3 ≤ (x + 2)/10 ≤ 0.5
Graph the solution set of the inequality, where x is an integer, on the number line.-2 < 2x + 3 < 6
Graph the solution set of the inequality, where x is an integer, on the number line.1 > -x > - 6
Graph the solution set of the inequality, where x is an integer, on the number line.-2 ≤ x < 6
Graph the solution set of the inequality, where x is an integer, on the number line.5(x + 4) - 6 ≤ 2x + 8
Graph the solution set of the inequality, where x is an integer, on the number line.-2(x - 1) < 3(x - 4) + 5
Graph the solution set of the inequality, where x is an integer, on the number line.3 (x + 4) ≥ 4x + 13
Graph the solution set of the inequality, where x is an integer, on the number line.-5x - 1 < 17 - 2x
Graph the solution set of the inequality, where x is an integer, on the number line.-15 < -4x - 3
Graph the solution set of the inequality, where x is an integer, on the number line.3x/5 ≤ 3
Graph the solution set of the inequality, where x is an integer, on the number line.-x/4 ≥ 2
Graph the solution set of the inequality, where x is an integer, on the number line.x/4 ≥ -3
Graph the solution set of the inequality, where x is an integer, on the number line.x/3 ≤ - 2
Graph the solution set of the inequality, where x is an integer, on the number line.x + 9 > 5
Graph the solution set of the inequality, where x is an integer, on the number line.x - 6 < -4
Graph the solution set of the inequality, where x is an integer, on the number line.5x ≥ 45
Graph the solution set of the inequality, where x is an integer, on the number line.-4x ≤ 36
Graph the solution set of the inequality, where x is an integer, on the number line.-2 < x
Graph the solution set of the inequality, where x is an integer, on the number line.x > 1
Graph the solution set of the inequality, where x is a real number, on the number line.1/2 < (x + 4)/2 ≤ 4
Graph the solution set of the inequality, where x is a real number, on the number line.2 < x - 4 ≤ 6
In a specific region of the country, the amount of a customer’s water bill, W, is directly proportional to the average daily temperature for the month, T, the lawn area, A, and the square root of
An article in the magazine Outdoor and Travel Photography states, €œIf a surface is illuminated by a point-source of light, the intensity of illumination produced is inversely proportional
(a) Assume a varies directly as b2. If bis doubled, how will it affect a? (b) Assume a varies inversely as b2. If bis doubled, how will it affect a?
(a) Assume y varies directly as x. If xis doubled, how will it affect y?(b) Assume y varies inversely as x. If xis doubled, how will it affect y?
(a) If y varies inversely as x and the constant of proportionality is 0.3, does x vary directly or inversely as y?(b) Give the new constant of proportionality as x varies inversely as y.
(a) If y varies directly as x and the constant of proportionality is 2, does x vary directly or inversely as y?(b) Give the new constant of proportionality as x varies directly as y.
The number of phone calls between two cities during a given time period, N, varies directly as the populations p1 and p2 of the two cities and inversely to the distance, d, between them. If 100,000
The wattage rating of an appliance, W, varies jointly as the square of the current, I, and the resistance, R. If the wattage is 6 watts when the current is 0.2 ampere and the resistance is 150 ohms,
The number of vibrations per second, v, of a guitar string varies directly as the square root of the tension, t, and inversely as the length of the string, l. If the number of vibrations per second
The electrical resistance of a wire, R, varies directly as its length, L, and inversely as its cross-sectional area, A. If the resistance of a wire is 0.2 ohm when the length is 200 ft and its
The stopping distance, d, of a car after the brakes are applied varies directly as the square of the speed, s, of the car. If a car traveling at a speed of 40 miles per hour can stop in 80 feet, what
The distance, d, that a rock falls when dropped from a cliff varies directly as the square of time, t, the rock is falling. If a rock falls 64 feet in 2 seconds, how far will it fall in 3 seconds?(a)
The volume of a gas, V, varies inversely as its pressure, P. If the volume of a gas is 6400 cubic centimeters (cc) when the pressure is 25 millimeters (mm) of mercury, determine the volume when the
The time, t, for an ice cube to melt is inversely proportional to the temperature, T, of the water in which the ice cube is placed. If it takes an ice cube 2 minutes to melt in 75°F water, how
The property tax, t, on a home is directly proportional to the assessed value, v,of the home. If the property tax on a home with an assessed value of $140,000 is $2100, what is the property tax on a
The profit, p,from selling bicycles is directly proportional to n, the number of bicycles sold. If the profit from selling 8 bicycles is $450, determine the profit from selling 18 bicycles.(a) Write
(a) Write the variation equation(b) Determine the quantity indicated.F varies jointly as q1 and q2 and inversely as the square of d. If F = 80 when q1 = 4, q2 = 16, and d = 0.4, determine F when
(a) Write the variation equation(b) Determine the quantity indicated.F varies jointly as M1 and M2 and inversely as the square of d. If F = 20 when M1 = 5, M2 = 10, and d = 0.2, determine F when M1 =
(a) Write the variation equation(b) Determine the quantity indicated.S varies jointly as I and the square of T. If S = 4 when I = 10 and T = 4, determine S when I = 4 and T = 6.
(a) Write the variation equation(b) Determine the quantity indicated.Z varies jointly as W and Y. If Z = 12 when W = 9 and Y = 4, determine Z when W = 50 and Y = 6.
(a) Write the variation equation(b) Determine the quantity indicated.A varies directly as the square of B. If A = 245 when B = 7, determine A when B = 12.
(a) Write the variation equation(b) Determine the quantity indicated.y varies directly as the square root of t and inversely as s. If y = 12 when t = 36 and s = 2, determine y when t = 81 and s = 4.
(a) Write the variation equation(b) Determine the quantity indicated.C varies inversely as J. If C = 7 when J = 0.7,determine C when J = 14.
(a) Write the variation equation(b) Determine the quantity indicated.H varies directly as L. If H = 12 when L = 40, determine H when L = 10.
(a) Write the variation equation(b) Determine the quantity indicated.A varies jointly as R1 and R2 and inversely as the square of L. Determine A when R1 = 120, R2 = 8, L = 5, and k = 3/2.
(a) Write the variation equation(b) Determine the quantity indicated.F varies jointly as D and E. Determine F when D = 3, E = 10, and k = 7.
(a) Write the variation equation(b) Determine the quantity indicated.M varies directly as J and inversely as C. Determine M when J = 12, C = 16, and k = 4.
(a) Write the variation equation(b) Determine the quantity indicated.A varies directly as B and inversely as C. Determine A when B = 5, C = 10, and k = 5.
(a) Write the variation equation(b) Determine the quantity indicated.r varies directly as the square of s. Determine r when s = 2 and k = 13.
The pressure, P, in pounds per square inch (psi) exerted on an object x ft below the sea is given by the equation P = 14.70 + 0.43x. The 14.70 represents the weight in pounds of the column of air
(a) Explain why -x2 will always be a negative number for any nonzero real number selected for x.(b) Explain why (-x2) will always be a positive number for any nonzero real number selected for x.
Suppose n represents any natural number. Explain why 1n equals 1.
Does (x + y)2= x2+ y2? Complete the table and state your conclusion. x? + y2 (x + y)² y 3 -3 3 -2 -2 -3 2.
Explain why (-1)n = 1 for any even number n.
A diver jumps from a platform diving board that is 32 feet above water. The height, h, of the diver above water, in feet, t seconds after jumping from the platform, can be determined by the equation
The time, t, in minutes, needed for clothes hanging on a line outdoors to dry, at a specific temperature, depends on the humidity, h. The time can be approximated by the equation t =2h2 + 80h +
The cost, c, in dollars, for Crescent City Tours to provide a tour for x people can be determined by the equation c = 220 + 2.75 x. Determine the cost for Crescent City Tours to provide a tour for 75
If the sales tax, s, on an item is 8%, the sales tax on an item costing d dollars can be found by the equation s = 0.08d. Determine the sales tax on a pair of sneakers that cost $79.
Solve the equation.5x + 0.050 = -0.732
Solve the equation.4(t - 3) + 8 = 4(2t - 6)
Solve the equation.4(3n + 1) = 5(4n - 6) + 9n
Solve the equation.6x + 8 - 22x = 28 + 14x - 10 + 12x
Solve the equation.3x + 2 - 6x = -x - 15 + 8 - 5x
Solve the equation.2/3(x - 4) = 1/4(x + 1)
Solve the equation.1/3(x + 3) = 2/5(x + 2)
Solve the equation.6(t + 2) - 14 = 6t - 2
Solve the equation.4(x - 4) + 12 = 4(x - 1)
Solve the equation.3(x + 2) - 4 = 2(x - 4)
Solve the equation.2(x + 3) - 4 = 2(x - 4)
Solve the equation.r/3 + 2r = 7
Solve the equation.x/4 + 2x = 1/3
Solve the equation.6t - 7 = 8t + 9
Solve the equation.6t - 8 = 4t - 2
Solve the equation.Solve the equation.0.9x - 1.2 = 2.4
Solve the equation.(1/2)y + 1/3 = 1/4
Solve the equation.(1/2)x + 1/3 = 2/3
Solve the equation.25 = 4x + 5
Solve the equation.16 = -3t - 2
Solve the equation.y - 4 = 13
Solve the equation.y + 7 = 9
Combine like terms.n - 3/4 + (5/9)n - 1/6
Combine like terms.(1/4)x + 4/5 - (2/3)x
Combine like terms.2/3(3x + 9) - 1/4 (2x + 5)
Combine like terms.2/3(x + 6) + 1/6(x + 6)
Combine like terms.0.9(2.3x - 2) + 1.7(3.2x - 5)
Combine like terms.0.2(x + 4) + 1.2(x - 3)
Combine like terms.6(r - 3) - 2(r + 5) + 10
Combine like terms.3(t + 3) + 5(t - 2) + 1
Combine like terms.2p - 4q - 3p + 4q - 15

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